Rhombidodecadodecahedron

In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38.

[1] It is given a Schläfli symbol t0,2{5⁄2,5}, and by the Wythoff construction this polyhedron can also be named a cantellated great dodecahedron.

Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms.

The medial deltoidal hexecontahedron (or midly lanceal ditriacontahedron) is a nonconvex isohedral polyhedron.